Given the Number 12,994,800, Calculate (Find) All the Factors (All the Divisors) of the Number 12,994,800 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 12,994,800

1. Carry out the prime factorization of the number 12,994,800:

The prime factorization of a number: finding the prime numbers that multiply together to make that number.

12,994,800 = 24 × 3 × 52 × 72 × 13 × 17
12,994,800 is not a prime number but a composite one.

» Online calculator. Check whether a number is prime or not. The prime factorization of composite numbers

* Prime number: a natural number that is divisible (divided evenly) only by 1 and itself. A prime number has exactly two factors: 1 and the number itself.
* Composite number: a natural number that has at least one other factor than 1 and itself.


2. Multiply the prime factors of the number 12,994,800

Multiply the prime factors involved in the prime factorization of the number in all their unique combinations, that give different results.

Also consider the exponents of these prime factors.

Also add 1 to the list of factors (divisors). All the numbers are divisible by 1.


All the factors (divisors) are listed below - in ascending order

The list of factors (divisors):

neither prime nor composite = 1
prime factor = 2
prime factor = 3
22 = 4
prime factor = 5
2 × 3 = 6
prime factor = 7
23 = 8
2 × 5 = 10
22 × 3 = 12
prime factor = 13
2 × 7 = 14
3 × 5 = 15
24 = 16
prime factor = 17
22 × 5 = 20
3 × 7 = 21
23 × 3 = 24
52 = 25
2 × 13 = 26
22 × 7 = 28
2 × 3 × 5 = 30
2 × 17 = 34
5 × 7 = 35
3 × 13 = 39
23 × 5 = 40
2 × 3 × 7 = 42
24 × 3 = 48
72 = 49
2 × 52 = 50
3 × 17 = 51
22 × 13 = 52
23 × 7 = 56
22 × 3 × 5 = 60
5 × 13 = 65
22 × 17 = 68
2 × 5 × 7 = 70
3 × 52 = 75
2 × 3 × 13 = 78
24 × 5 = 80
22 × 3 × 7 = 84
5 × 17 = 85
7 × 13 = 91
2 × 72 = 98
22 × 52 = 100
2 × 3 × 17 = 102
23 × 13 = 104
3 × 5 × 7 = 105
24 × 7 = 112
7 × 17 = 119
23 × 3 × 5 = 120
2 × 5 × 13 = 130
23 × 17 = 136
22 × 5 × 7 = 140
3 × 72 = 147
2 × 3 × 52 = 150
22 × 3 × 13 = 156
23 × 3 × 7 = 168
2 × 5 × 17 = 170
52 × 7 = 175
2 × 7 × 13 = 182
3 × 5 × 13 = 195
22 × 72 = 196
23 × 52 = 200
22 × 3 × 17 = 204
24 × 13 = 208
2 × 3 × 5 × 7 = 210
13 × 17 = 221
2 × 7 × 17 = 238
24 × 3 × 5 = 240
5 × 72 = 245
3 × 5 × 17 = 255
22 × 5 × 13 = 260
24 × 17 = 272
3 × 7 × 13 = 273
23 × 5 × 7 = 280
2 × 3 × 72 = 294
22 × 3 × 52 = 300
23 × 3 × 13 = 312
52 × 13 = 325
24 × 3 × 7 = 336
22 × 5 × 17 = 340
2 × 52 × 7 = 350
3 × 7 × 17 = 357
22 × 7 × 13 = 364
2 × 3 × 5 × 13 = 390
23 × 72 = 392
24 × 52 = 400
23 × 3 × 17 = 408
22 × 3 × 5 × 7 = 420
52 × 17 = 425
2 × 13 × 17 = 442
5 × 7 × 13 = 455
22 × 7 × 17 = 476
2 × 5 × 72 = 490
2 × 3 × 5 × 17 = 510
23 × 5 × 13 = 520
3 × 52 × 7 = 525
2 × 3 × 7 × 13 = 546
24 × 5 × 7 = 560
22 × 3 × 72 = 588
5 × 7 × 17 = 595
23 × 3 × 52 = 600
24 × 3 × 13 = 624
72 × 13 = 637
2 × 52 × 13 = 650
3 × 13 × 17 = 663
23 × 5 × 17 = 680
22 × 52 × 7 = 700
2 × 3 × 7 × 17 = 714
23 × 7 × 13 = 728
3 × 5 × 72 = 735
22 × 3 × 5 × 13 = 780
24 × 72 = 784
24 × 3 × 17 = 816
72 × 17 = 833
23 × 3 × 5 × 7 = 840
2 × 52 × 17 = 850
22 × 13 × 17 = 884
2 × 5 × 7 × 13 = 910
23 × 7 × 17 = 952
3 × 52 × 13 = 975
22 × 5 × 72 = 980
22 × 3 × 5 × 17 = 1,020
24 × 5 × 13 = 1,040
2 × 3 × 52 × 7 = 1,050
22 × 3 × 7 × 13 = 1,092
5 × 13 × 17 = 1,105
23 × 3 × 72 = 1,176
2 × 5 × 7 × 17 = 1,190
24 × 3 × 52 = 1,200
52 × 72 = 1,225
2 × 72 × 13 = 1,274
3 × 52 × 17 = 1,275
22 × 52 × 13 = 1,300
2 × 3 × 13 × 17 = 1,326
24 × 5 × 17 = 1,360
3 × 5 × 7 × 13 = 1,365
23 × 52 × 7 = 1,400
22 × 3 × 7 × 17 = 1,428
24 × 7 × 13 = 1,456
2 × 3 × 5 × 72 = 1,470
7 × 13 × 17 = 1,547
23 × 3 × 5 × 13 = 1,560
2 × 72 × 17 = 1,666
24 × 3 × 5 × 7 = 1,680
22 × 52 × 17 = 1,700
23 × 13 × 17 = 1,768
3 × 5 × 7 × 17 = 1,785
22 × 5 × 7 × 13 = 1,820
24 × 7 × 17 = 1,904
3 × 72 × 13 = 1,911
2 × 3 × 52 × 13 = 1,950
23 × 5 × 72 = 1,960
23 × 3 × 5 × 17 = 2,040
22 × 3 × 52 × 7 = 2,100
23 × 3 × 7 × 13 = 2,184
2 × 5 × 13 × 17 = 2,210
52 × 7 × 13 = 2,275
24 × 3 × 72 = 2,352
22 × 5 × 7 × 17 = 2,380
2 × 52 × 72 = 2,450
3 × 72 × 17 = 2,499
22 × 72 × 13 = 2,548
2 × 3 × 52 × 17 = 2,550
23 × 52 × 13 = 2,600
22 × 3 × 13 × 17 = 2,652
2 × 3 × 5 × 7 × 13 = 2,730
24 × 52 × 7 = 2,800
23 × 3 × 7 × 17 = 2,856
22 × 3 × 5 × 72 = 2,940
52 × 7 × 17 = 2,975
2 × 7 × 13 × 17 = 3,094
24 × 3 × 5 × 13 = 3,120
5 × 72 × 13 = 3,185
3 × 5 × 13 × 17 = 3,315
22 × 72 × 17 = 3,332
23 × 52 × 17 = 3,400
24 × 13 × 17 = 3,536
2 × 3 × 5 × 7 × 17 = 3,570
This list continues below...

... This list continues from above
23 × 5 × 7 × 13 = 3,640
3 × 52 × 72 = 3,675
2 × 3 × 72 × 13 = 3,822
22 × 3 × 52 × 13 = 3,900
24 × 5 × 72 = 3,920
24 × 3 × 5 × 17 = 4,080
5 × 72 × 17 = 4,165
23 × 3 × 52 × 7 = 4,200
24 × 3 × 7 × 13 = 4,368
22 × 5 × 13 × 17 = 4,420
2 × 52 × 7 × 13 = 4,550
3 × 7 × 13 × 17 = 4,641
23 × 5 × 7 × 17 = 4,760
22 × 52 × 72 = 4,900
2 × 3 × 72 × 17 = 4,998
23 × 72 × 13 = 5,096
22 × 3 × 52 × 17 = 5,100
24 × 52 × 13 = 5,200
23 × 3 × 13 × 17 = 5,304
22 × 3 × 5 × 7 × 13 = 5,460
52 × 13 × 17 = 5,525
24 × 3 × 7 × 17 = 5,712
23 × 3 × 5 × 72 = 5,880
2 × 52 × 7 × 17 = 5,950
22 × 7 × 13 × 17 = 6,188
2 × 5 × 72 × 13 = 6,370
2 × 3 × 5 × 13 × 17 = 6,630
23 × 72 × 17 = 6,664
24 × 52 × 17 = 6,800
3 × 52 × 7 × 13 = 6,825
22 × 3 × 5 × 7 × 17 = 7,140
24 × 5 × 7 × 13 = 7,280
2 × 3 × 52 × 72 = 7,350
22 × 3 × 72 × 13 = 7,644
5 × 7 × 13 × 17 = 7,735
23 × 3 × 52 × 13 = 7,800
2 × 5 × 72 × 17 = 8,330
24 × 3 × 52 × 7 = 8,400
23 × 5 × 13 × 17 = 8,840
3 × 52 × 7 × 17 = 8,925
22 × 52 × 7 × 13 = 9,100
2 × 3 × 7 × 13 × 17 = 9,282
24 × 5 × 7 × 17 = 9,520
3 × 5 × 72 × 13 = 9,555
23 × 52 × 72 = 9,800
22 × 3 × 72 × 17 = 9,996
24 × 72 × 13 = 10,192
23 × 3 × 52 × 17 = 10,200
24 × 3 × 13 × 17 = 10,608
72 × 13 × 17 = 10,829
23 × 3 × 5 × 7 × 13 = 10,920
2 × 52 × 13 × 17 = 11,050
24 × 3 × 5 × 72 = 11,760
22 × 52 × 7 × 17 = 11,900
23 × 7 × 13 × 17 = 12,376
3 × 5 × 72 × 17 = 12,495
22 × 5 × 72 × 13 = 12,740
22 × 3 × 5 × 13 × 17 = 13,260
24 × 72 × 17 = 13,328
2 × 3 × 52 × 7 × 13 = 13,650
23 × 3 × 5 × 7 × 17 = 14,280
22 × 3 × 52 × 72 = 14,700
23 × 3 × 72 × 13 = 15,288
2 × 5 × 7 × 13 × 17 = 15,470
24 × 3 × 52 × 13 = 15,600
52 × 72 × 13 = 15,925
3 × 52 × 13 × 17 = 16,575
22 × 5 × 72 × 17 = 16,660
24 × 5 × 13 × 17 = 17,680
2 × 3 × 52 × 7 × 17 = 17,850
23 × 52 × 7 × 13 = 18,200
22 × 3 × 7 × 13 × 17 = 18,564
2 × 3 × 5 × 72 × 13 = 19,110
24 × 52 × 72 = 19,600
23 × 3 × 72 × 17 = 19,992
24 × 3 × 52 × 17 = 20,400
52 × 72 × 17 = 20,825
2 × 72 × 13 × 17 = 21,658
24 × 3 × 5 × 7 × 13 = 21,840
22 × 52 × 13 × 17 = 22,100
3 × 5 × 7 × 13 × 17 = 23,205
23 × 52 × 7 × 17 = 23,800
24 × 7 × 13 × 17 = 24,752
2 × 3 × 5 × 72 × 17 = 24,990
23 × 5 × 72 × 13 = 25,480
23 × 3 × 5 × 13 × 17 = 26,520
22 × 3 × 52 × 7 × 13 = 27,300
24 × 3 × 5 × 7 × 17 = 28,560
23 × 3 × 52 × 72 = 29,400
24 × 3 × 72 × 13 = 30,576
22 × 5 × 7 × 13 × 17 = 30,940
2 × 52 × 72 × 13 = 31,850
3 × 72 × 13 × 17 = 32,487
2 × 3 × 52 × 13 × 17 = 33,150
23 × 5 × 72 × 17 = 33,320
22 × 3 × 52 × 7 × 17 = 35,700
24 × 52 × 7 × 13 = 36,400
23 × 3 × 7 × 13 × 17 = 37,128
22 × 3 × 5 × 72 × 13 = 38,220
52 × 7 × 13 × 17 = 38,675
24 × 3 × 72 × 17 = 39,984
2 × 52 × 72 × 17 = 41,650
22 × 72 × 13 × 17 = 43,316
23 × 52 × 13 × 17 = 44,200
2 × 3 × 5 × 7 × 13 × 17 = 46,410
24 × 52 × 7 × 17 = 47,600
3 × 52 × 72 × 13 = 47,775
22 × 3 × 5 × 72 × 17 = 49,980
24 × 5 × 72 × 13 = 50,960
24 × 3 × 5 × 13 × 17 = 53,040
5 × 72 × 13 × 17 = 54,145
23 × 3 × 52 × 7 × 13 = 54,600
24 × 3 × 52 × 72 = 58,800
23 × 5 × 7 × 13 × 17 = 61,880
3 × 52 × 72 × 17 = 62,475
22 × 52 × 72 × 13 = 63,700
2 × 3 × 72 × 13 × 17 = 64,974
22 × 3 × 52 × 13 × 17 = 66,300
24 × 5 × 72 × 17 = 66,640
23 × 3 × 52 × 7 × 17 = 71,400
24 × 3 × 7 × 13 × 17 = 74,256
23 × 3 × 5 × 72 × 13 = 76,440
2 × 52 × 7 × 13 × 17 = 77,350
22 × 52 × 72 × 17 = 83,300
23 × 72 × 13 × 17 = 86,632
24 × 52 × 13 × 17 = 88,400
22 × 3 × 5 × 7 × 13 × 17 = 92,820
2 × 3 × 52 × 72 × 13 = 95,550
23 × 3 × 5 × 72 × 17 = 99,960
2 × 5 × 72 × 13 × 17 = 108,290
24 × 3 × 52 × 7 × 13 = 109,200
3 × 52 × 7 × 13 × 17 = 116,025
24 × 5 × 7 × 13 × 17 = 123,760
2 × 3 × 52 × 72 × 17 = 124,950
23 × 52 × 72 × 13 = 127,400
22 × 3 × 72 × 13 × 17 = 129,948
23 × 3 × 52 × 13 × 17 = 132,600
24 × 3 × 52 × 7 × 17 = 142,800
24 × 3 × 5 × 72 × 13 = 152,880
22 × 52 × 7 × 13 × 17 = 154,700
3 × 5 × 72 × 13 × 17 = 162,435
23 × 52 × 72 × 17 = 166,600
24 × 72 × 13 × 17 = 173,264
23 × 3 × 5 × 7 × 13 × 17 = 185,640
22 × 3 × 52 × 72 × 13 = 191,100
24 × 3 × 5 × 72 × 17 = 199,920
22 × 5 × 72 × 13 × 17 = 216,580
2 × 3 × 52 × 7 × 13 × 17 = 232,050
22 × 3 × 52 × 72 × 17 = 249,900
24 × 52 × 72 × 13 = 254,800
23 × 3 × 72 × 13 × 17 = 259,896
24 × 3 × 52 × 13 × 17 = 265,200
52 × 72 × 13 × 17 = 270,725
23 × 52 × 7 × 13 × 17 = 309,400
2 × 3 × 5 × 72 × 13 × 17 = 324,870
24 × 52 × 72 × 17 = 333,200
24 × 3 × 5 × 7 × 13 × 17 = 371,280
23 × 3 × 52 × 72 × 13 = 382,200
23 × 5 × 72 × 13 × 17 = 433,160
22 × 3 × 52 × 7 × 13 × 17 = 464,100
23 × 3 × 52 × 72 × 17 = 499,800
24 × 3 × 72 × 13 × 17 = 519,792
2 × 52 × 72 × 13 × 17 = 541,450
24 × 52 × 7 × 13 × 17 = 618,800
22 × 3 × 5 × 72 × 13 × 17 = 649,740
24 × 3 × 52 × 72 × 13 = 764,400
3 × 52 × 72 × 13 × 17 = 812,175
24 × 5 × 72 × 13 × 17 = 866,320
23 × 3 × 52 × 7 × 13 × 17 = 928,200
24 × 3 × 52 × 72 × 17 = 999,600
22 × 52 × 72 × 13 × 17 = 1,082,900
23 × 3 × 5 × 72 × 13 × 17 = 1,299,480
2 × 3 × 52 × 72 × 13 × 17 = 1,624,350
24 × 3 × 52 × 7 × 13 × 17 = 1,856,400
23 × 52 × 72 × 13 × 17 = 2,165,800
24 × 3 × 5 × 72 × 13 × 17 = 2,598,960
22 × 3 × 52 × 72 × 13 × 17 = 3,248,700
24 × 52 × 72 × 13 × 17 = 4,331,600
23 × 3 × 52 × 72 × 13 × 17 = 6,497,400
24 × 3 × 52 × 72 × 13 × 17 = 12,994,800

The final answer:
(scroll down)

12,994,800 has 360 factors (divisors):
1; 2; 3; 4; 5; 6; 7; 8; 10; 12; 13; 14; 15; 16; 17; 20; 21; 24; 25; 26; 28; 30; 34; 35; 39; 40; 42; 48; 49; 50; 51; 52; 56; 60; 65; 68; 70; 75; 78; 80; 84; 85; 91; 98; 100; 102; 104; 105; 112; 119; 120; 130; 136; 140; 147; 150; 156; 168; 170; 175; 182; 195; 196; 200; 204; 208; 210; 221; 238; 240; 245; 255; 260; 272; 273; 280; 294; 300; 312; 325; 336; 340; 350; 357; 364; 390; 392; 400; 408; 420; 425; 442; 455; 476; 490; 510; 520; 525; 546; 560; 588; 595; 600; 624; 637; 650; 663; 680; 700; 714; 728; 735; 780; 784; 816; 833; 840; 850; 884; 910; 952; 975; 980; 1,020; 1,040; 1,050; 1,092; 1,105; 1,176; 1,190; 1,200; 1,225; 1,274; 1,275; 1,300; 1,326; 1,360; 1,365; 1,400; 1,428; 1,456; 1,470; 1,547; 1,560; 1,666; 1,680; 1,700; 1,768; 1,785; 1,820; 1,904; 1,911; 1,950; 1,960; 2,040; 2,100; 2,184; 2,210; 2,275; 2,352; 2,380; 2,450; 2,499; 2,548; 2,550; 2,600; 2,652; 2,730; 2,800; 2,856; 2,940; 2,975; 3,094; 3,120; 3,185; 3,315; 3,332; 3,400; 3,536; 3,570; 3,640; 3,675; 3,822; 3,900; 3,920; 4,080; 4,165; 4,200; 4,368; 4,420; 4,550; 4,641; 4,760; 4,900; 4,998; 5,096; 5,100; 5,200; 5,304; 5,460; 5,525; 5,712; 5,880; 5,950; 6,188; 6,370; 6,630; 6,664; 6,800; 6,825; 7,140; 7,280; 7,350; 7,644; 7,735; 7,800; 8,330; 8,400; 8,840; 8,925; 9,100; 9,282; 9,520; 9,555; 9,800; 9,996; 10,192; 10,200; 10,608; 10,829; 10,920; 11,050; 11,760; 11,900; 12,376; 12,495; 12,740; 13,260; 13,328; 13,650; 14,280; 14,700; 15,288; 15,470; 15,600; 15,925; 16,575; 16,660; 17,680; 17,850; 18,200; 18,564; 19,110; 19,600; 19,992; 20,400; 20,825; 21,658; 21,840; 22,100; 23,205; 23,800; 24,752; 24,990; 25,480; 26,520; 27,300; 28,560; 29,400; 30,576; 30,940; 31,850; 32,487; 33,150; 33,320; 35,700; 36,400; 37,128; 38,220; 38,675; 39,984; 41,650; 43,316; 44,200; 46,410; 47,600; 47,775; 49,980; 50,960; 53,040; 54,145; 54,600; 58,800; 61,880; 62,475; 63,700; 64,974; 66,300; 66,640; 71,400; 74,256; 76,440; 77,350; 83,300; 86,632; 88,400; 92,820; 95,550; 99,960; 108,290; 109,200; 116,025; 123,760; 124,950; 127,400; 129,948; 132,600; 142,800; 152,880; 154,700; 162,435; 166,600; 173,264; 185,640; 191,100; 199,920; 216,580; 232,050; 249,900; 254,800; 259,896; 265,200; 270,725; 309,400; 324,870; 333,200; 371,280; 382,200; 433,160; 464,100; 499,800; 519,792; 541,450; 618,800; 649,740; 764,400; 812,175; 866,320; 928,200; 999,600; 1,082,900; 1,299,480; 1,624,350; 1,856,400; 2,165,800; 2,598,960; 3,248,700; 4,331,600; 6,497,400 and 12,994,800
out of which 6 prime factors: 2; 3; 5; 7; 13 and 17
12,994,800 and 1 are sometimes called improper factors, the others are called proper factors (proper divisors).

A quick way to find the factors (the divisors) of a number is to break it down into prime factors.

Then multiply the prime factors and their exponents, if any, in all their different combinations.


Other similar operations of calculating factors (divisors):

» What are all the proper, improper and prime factors (divisors) of the number 12,994,788?

» What are all the proper, improper and prime factors (divisors) of the number 12,994,801?


Calculate all the divisors (factors) of the given numbers

How to calculate (find) all the factors (divisors) of a number:

Break down the number into prime factors. Then multiply its prime factors in all their unique combinations, that give different results.

To calculate the common factors of two numbers:

The common factors (divisors) of two numbers are all the factors of the greatest common factor, gcf.

Calculate the greatest (highest) common factor (divisor) of the two numbers, gcf (hcf, gcd).

Break down the GCF into prime factors. Then multiply its prime factors in all their unique combinations, that give different results.

The latest 10 sets of calculated factors (divisors): of one number or the common factors of two numbers

What are all the proper, improper and prime factors (all the divisors) of the number 12,994,800? How to calculate them? Apr 29 15:23 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 2,048,000? How to calculate them? Apr 29 15:23 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 102,949,600? How to calculate them? Apr 29 15:23 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 5,201,664? How to calculate them? Apr 29 15:23 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 75,517? How to calculate them? Apr 29 15:23 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 131,302? How to calculate them? Apr 29 15:23 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 771,710? How to calculate them? Apr 29 15:23 UTC (GMT)
What are all the common factors (all the divisors and the prime factors) of the numbers 392 and 48? How to calculate them? Apr 29 15:23 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 712,248? How to calculate them? Apr 29 15:23 UTC (GMT)
What are all the proper, improper and prime factors (all the divisors) of the number 2,159,040? How to calculate them? Apr 29 15:23 UTC (GMT)
The list of all the calculated factors (divisors) of one or two numbers

Factors (divisors), common factors (common divisors), the greatest common factor, GCF (also called the greatest common divisor, GCD, or the highest common factor, HCF)

  • If the number "t" is a factor (divisor) of the number "a" then in the prime factorization of "t" we will only encounter prime factors that also occur in the prime factorization of "a".
  • If there are exponents involved, the maximum value of an exponent for any base of a power that is found in the prime factorization of "t" (powers, or multiplicities) is at most equal to the exponent of the same base that is involved in the prime factorization of "a".
  • Hint: 23 = 2 × 2 × 2 = 8. 2 is called the base and 3 is the exponent. 23 is the power and 8 is the value of the power. We sometimes say that the number 2 is raised to the power of 3.
  • For example, 12 is a factor (divisor) of 120 - the remainder is zero when dividing 120 by 12.
  • Let's look at the prime factorization of both numbers and notice the bases and the exponents that occur in the prime factorization of both numbers:
  • 12 = 2 × 2 × 3 = 22 × 3
  • 120 = 2 × 2 × 2 × 3 × 5 = 23 × 3 × 5
  • 120 contains all the prime factors of 12, and all its bases' exponents are higher than those of 12.
  • If "t" is a common factor (divisor) of "a" and "b", then the prime factorization of "t" contains only the common prime factors involved in the prime factorizations of both "a" and "b".
  • If there are exponents involved, the maximum value of an exponent for any base of a power that is found in the prime factorization of "t" is at most equal to the minimum of the exponents of the same base that is involved in the prime factorization of both "a" and "b".
  • For example, 12 is the common factor of 48 and 360.
  • The remainder is zero when dividing either 48 or 360 by 12.
  • Here there are the prime factorizations of the three numbers, 12, 48 and 360:
  • 12 = 22 × 3
  • 48 = 24 × 3
  • 360 = 23 × 32 × 5
  • Please note that 48 and 360 have more factors (divisors): 2, 3, 4, 6, 8, 12, 24. Among them, 24 is the greatest common factor, GCF (or the greatest common divisor, GCD, or the highest common factor, HCF) of 48 and 360.
  • The greatest common factor, GCF, of two numbers, "a" and "b", is the product of all the common prime factors involved in the prime factorizations of both "a" and "b", taken by the lowest exponents.
  • Based on this rule it is calculated the greatest common factor, GCF, (or the greatest common divisor GCD, HCF) of several numbers, as shown in the example below...
  • GCF, GCD (1,260; 3,024; 5,544) = ?
  • 1,260 = 22 × 32
  • 3,024 = 24 × 32 × 7
  • 5,544 = 23 × 32 × 7 × 11
  • The common prime factors are:
  • 2 - its lowest exponent (multiplicity) is: min.(2; 3; 4) = 2
  • 3 - its lowest exponent (multiplicity) is: min.(2; 2; 2) = 2
  • GCF, GCD (1,260; 3,024; 5,544) = 22 × 32 = 252
  • Coprime numbers:
  • If two numbers "a" and "b" have no other common factors (divisors) than 1, gfc, gcd, hcf (a; b) = 1, then the numbers "a" and "b" are called coprime (or relatively prime).
  • Factors of the GCF
  • If "a" and "b" are not coprime, then every common factor (divisor) of "a" and "b" is a also a factor (divisor) of the greatest common factor, GCF (greatest common divisor, GCD, highest common factor, HCF) of "a" and "b".